Dynamical possibilities to design Earth-to-Moon transfers in the patched-three body approximation

Abstract

This paper concerns Earth-to-Moon transfers in the patched three-body approximation, in which the Sun-Earth-Moon-Spacecraft system is modeled by two coupled Restricted Three-Body Problems. The standard transfers in this approach are manifold guided solutions, connecting transit and non-transit orbits of each three-body system. These are lowenergy solutions but require long transfer time, usually more than 100 days. We present alternative solutions in the Sun-Earth portion of the transfer that reduce total transfer time to about 10 days, while still providing lunar ballistic capture at arrival. Instead of connecting transit and non-transit orbits, these alternative transfer solutions connect a bi-parametric family of quasi-periodic orbits around the Earth in the Sun-Earth system with transit orbits of the Earth-Moon system. We investigate coupling possibilities in view of the Jacobi constant of the three-body systems and illustrate the alternative patching solutions. Due to the quasi-periodic nature of the orbits in the first part of the transfer, these alternative solutions provide new dynamical possibilities in the patched three-body approximation, even when the hyperbolic invariant manifolds of the coupled three-body systems do not intersect properly.